The present invention is generally directed to digital circuits. More particularly, the present invention is directed to a digital circuit for multiplying a sampled digitized data input signal by the cosine or sine function.
In digital circuit applications it is often desirable to be able to multiply an input signal by the cosine or sine function. This is particularly desirable in the manipulation of digitized radio frequency signals wherein it is desirable to be able to produce in-phase and quadrature-phase signal components. Typically such multiplication is accomplished by the utilization of straight forward digital multiplication circuits. In general, digital multiplication can be a relatively complicated process requiring significant amounts of circuitry.
However, the present applicant has discerned that by utilization of a sampling rate which is six times the carrier frequency, it is possible to construct extremely simple cosine and sine multiplication circuits which require only a shifter and an inverter which are controlled to produce the desired cosine multiplication function.
A digital cosine multiplication circuit of the present invention comprises a digital shifting circuit which receives the sampled input signal. This shifting circuit supplies its output to a digital inverting circuit which produces the desired results. The multiplication circuit includes control means for selecting whether or not the shifting circuit operates to shift by one bit position or not to shift at all. Additionally the control means operates to control whether or not the digital inverting circuit produces an inverted or a non-inverted output. Several different embodiments for this circuit are illustrated. In particular, one such embodiment is implemented by means of a pair of multiplexor circuits.
As will be seen by an analysis of the relevant multiplication coefficients, the circuit is best implemented in the fashion described above. However, as a consequence of the arithmetic values of the coefficients it is clearly significantly easier to have multiplied the usually necessary coefficients by a factor of 2. Accordingly, this introduces an extra scaling factor in the output signal. However, this output signal scaling factor is 2 and accordingly, it is readily compensated for by means of a simple shifting circuit. This shifting circuit is optional depending on the further digital signal processing applied to the result.
As will also be seen by an analysis of the sine function, the utilization of a sampling frequency which is sic times the carrier frequency also results in a set of multiplication which are easily implemented via very simple digital circuits. In fact, except for an amplitude factor which is typically not relevant for subsequent processing, the sine circuit is implementable with only an inverter and a multiplexor with an appropriate multiplexor controller.
Accordingly, it is an object of the present invention to provide circuits for digital multiplication involving the sine and cosine functions.
It is yet another object of the present invention to simplify the construction of digital circuits using which require in phase and quadrature-phase signals.
It is a still further object of the present invention to simplify the construction of certain digital multiplication circuits.
It is yet another object of the present invention to provide a simple and fast mechanism for sine and cosine multiplication.
The recitation herein of a list of desirable objects which are met by various embodiments of the present invention is not meant to imply or suggest that any or all of these objects are present as essential or necessary features, either individually or collectively, in the most general embodiment of the present invention or in any of its more specific embodiments.